Predicate calculus and program semantics
Predicate calculus and program semantics
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Type Classes and Overloading in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Two-Level Approach Towards Lean Proof-Checking
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
PVS: Combining Specification, Proof Checking, and Model Checking
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Calculational Reasoning Revisited (An Isabelle/Isar Experience)
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
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We present a complete formalization of the Hahn-Banach theorem in the simply-typed set-theory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for high-level reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.